Problem: Simplify the following expression: $k = \dfrac{6b + 10a}{8b + 2} - \dfrac{10c + 10b}{8b + 2}$ You can assume $a,b,c \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{6b + 10a - (10c + 10b)}{8b + 2}$ $k = \dfrac{-4b + 10a - 10c}{8b + 2}$ The numerator and denominator have a common factor of $2$, so we can simplify $k = \dfrac{-2b + 5a - 5c}{4b + 1}$